Finite-size effects in the nonphononic density of states in computer glasses

The universal form of the density of nonphononic, quasilocalized vibrational modes of frequency ω in structural glasses, D(ω), was predicted theoretically decades ago, but only recently revealed in numerical simulations. In particular, it has been recently established that, in generic computer glasses, D(ω) increases from zero frequency as ω₄, independent of spatial dimension and of microscopic details. However, it has been shown [Lerner and Bouchbinder, Phys. Rev. E 96, 020104(R) (2017)2470-004510.1103/PhysRevE.96.020104] that the preparation protocol employed to create glassy samples may affect the form of their resulting D(ω): glassy samples rapidly quenched from high-temperature liquid states were shown to feature D(ω)∼ω^β with β < 4, presumably limiting the degree of universality of the ω⁴ law. Here we show that exponents β < 4 are seen only in small glassy samples quenched from high-temperature liquid states - whose sizes are comparable to or smaller than the size of the disordered core of soft quasilocalized vibrations - while larger glassy samples made with the same protocol feature the universal ω⁴ law. Our results demonstrate that observations of β < 4 in the nonphononic density of states stem from finite-size effects, and we thus conclude that the ω⁴ law should be featured by any sufficiently large glass quenched from a melt.